A Drift-Diffusion-Schrödinger–Poisson system is presented, which models the transport of a quasi bidimensional electron gas confined in a nanostructure. We prove the existence of a unique solution to this nonlinear system. The proof makes use of some a priori estimates due to the physical structure of the problem, and also involves the resolution of a quasistatic Schrödinger–Poisson system.
Nous présentons un système de Dérive-Diffusion-Schrödinger–Poisson qui décrit le transport d'un gaz d'électrons confiné dans une nanostructure. Nous montrons que ce système admet une unique solution. Cette preuve d'existence est obtenue à l'aide d'estimations a priori dues à la nature physique du problème et passe par la résolution d'un système quasistatique de Schrödinger–Poisson.
Accepted:
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Naoufel Ben Abdallah 1; Florian Méhats 1; Nicolas Vauchelet 2
@article{CRMATH_2002__335_12_1007_0, author = {Naoufel Ben Abdallah and Florian M\'ehats and Nicolas Vauchelet}, title = {Analysis of a {Drift-Diffusion-Schr\"odinger{\textendash}Poisson} model}, journal = {Comptes Rendus. Math\'ematique}, pages = {1007--1012}, publisher = {Elsevier}, volume = {335}, number = {12}, year = {2002}, doi = {10.1016/S1631-073X(02)02612-2}, language = {en}, }
TY - JOUR AU - Naoufel Ben Abdallah AU - Florian Méhats AU - Nicolas Vauchelet TI - Analysis of a Drift-Diffusion-Schrödinger–Poisson model JO - Comptes Rendus. Mathématique PY - 2002 SP - 1007 EP - 1012 VL - 335 IS - 12 PB - Elsevier DO - 10.1016/S1631-073X(02)02612-2 LA - en ID - CRMATH_2002__335_12_1007_0 ER -
Naoufel Ben Abdallah; Florian Méhats; Nicolas Vauchelet. Analysis of a Drift-Diffusion-Schrödinger–Poisson model. Comptes Rendus. Mathématique, Volume 335 (2002) no. 12, pp. 1007-1012. doi : 10.1016/S1631-073X(02)02612-2. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02612-2/
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